3.1 & 3.2 Identify Pairs of Lines and Angles Use Parallel Lines and Transversals

NameDefinitionSlope Relationship Picture Parallel lines Intersecting lines Lines that never intersect. Same slope Lines that cross at one point Not same m = 2 then m = 2

Perp. lines Oblique lines Lines that cross forming right angles Intersecting lines that aren’t perpendicular Opposite AND reciprocal slopes m = 2 becomes m = – 1212 Not same Not opposite reciprocal

Coplanar Skew Lines on the same plane Lines that aren’t on the same plane and don’t intersect any

If there is a line and a point not on the line, then there is exactly one line through the given point parallel to the given line. Parallel Postulate P

If there is a line and a point not on the line, then there is exactly one line through the given point perpendicular to the given line. Perpendicular Postulate P

1. Use each of the vocabulary words to describe the picture.

NameDescriptionExample Transversal Line that intersects two or more coplanar lines at different points

Corresponding Angles Angles in the same relative position  1 &  5  2 &  6  3 &  7  4 &  8 Ex. top left

Alternate Interior Angles Angles on opposite sides of the transversal and inside the two other lines  4 &  5  3 &  6

Alternate Exterior Angles Angles on opposite sides of the transversal and outside the two other lines  1 &  8  2 &  7

Consecutive Interior Angles Angles on the same side of the transversal inside the other lines  3 &  5  4 &  6

If then something magical happens!!!!!!

NameIf, then Corresponding Angles  1   5  2   6  3   7  4   8

NameIf, then Alternate Interior Angles  4   5  3   6

NameIf, then Alternate Exterior Angles  1   8  2   7

NameIf, then Consecutive Interior Angles m  3 + m  5 = 180° m  4 + m  6 = 180°

Construct a Parallel Line through the point: P A

1. Find the values of x and y. Justify your answers. x = 80° Vertical angles 80° y = 80° Alternate Interior Angles

1. Find the values of x and y. Justify your answers. y = 120° Alternate Exterior Angles 120° 60° x = 60° Supplementary Angles

1. Find the values of x and y. Justify your answers. y = 130° Vertical Angles 130° 50° x = 50° Consecutive Interior Angles

2. Find the value of x. Alternate Interior Angles 2x = 80 x = 40°

2. Find the value of x. Corresponding Angles x – 10 = 100 x = 110°

2. Find the value of x. Consecutive Interior Angles 2x = 180 2x = 70 x = 35°

3. Decide whether the lines are parallel, perpendicular, or oblique. oblique perpendicular parallel perpendicular